Compressible Aerodynamic Flow Simulations Using ENO and WENO Schemes in a Finite Volume Unstructured Grid Context

W.R. Wolf, J.L.F. Azevedo


In this work the essentially non-oscillatory schemes (ENO) and the weighted essentially non-oscillatory schemes (WENO) are implemented in a cell centered finite volume context on unstructured grids. The 2-D Euler equations will be considered to represent the flows of interest. The ENO andWENO schemes have been developed with the purpose of accurately capturing discontinuities appearing in problems governed by hyperbolic conservation laws. In the high Mach number aerodynamic studies of interest, these discontinuities are mainly represented by shock waves. The entire reconstruction process of ENO and WENO schemes is described in detail for any order of accuracy with an emphasis to the implementation of the second-order accurate schemes. An agglomeration multigrid method is used to reach faster convergence to steady state. The solution of the transonic flow over a RAE2822 supercritical airfoil is presented in order to assess the capability implemented against data available in the literature.


[1] R. Abgrall, On essentially non-oscillatory schemes on unstructured meshes: analysis and implementation, Journal of Computational Physics, 114 (1994), 45-58.

W.K. Anderson, J.L. Thomas and B. van Leer, A comparison of finite volume flux vector splittings for the Euler equations, AIAA Journal 24 (1986), 1453-1460.

J.L.F. Azevedo and H. Korzenowski, Comparison of unstructured grid finite volume methods for cold gas hypersonic flow simulations, in “Proceedings of the 16th AIAA Applied Aerodynamics Conference”, Albuquerque, New Mexico, USA, AIAA Paper N◦. 98-2629, pp. 447-463, 1998.

J.L.F. Azevedo, L.F. Figueira da Silva and D. Strauss, Order of accuracy study of unstructured grid finite volume upwind schemes. Paper submitted to the Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2005.

M. Drela, A User Guide to MSES 2.92, MIT Computational Aerospace Sciences Laboratory, 1996.

O. Friedrich, Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids, Journal of Computational Physics, 144 (1998), 194-212.

C.F.O. Gooch, High order ENO schemes for unstructured meshes based on least-squares reconstruction, Argonne National Laboratory, Report N◦. P631-1296, Mathematics and Computer Science Division, 1997.

A. Harten, S. Osher, B. Engquist and S.R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes III, Journal of Computational Physics, 71 (1987), 231-303.

C. Hu and C.W. Shu, Weighted essentially non-oscillatory schemes on triangular meshes, Journal of Computational Physics, 150 (1999), 97-127.

G.S. Jiang and C.W. Shu, Efficient implementation of weighted ENO schemes, Journal of Computational Physics, 126 (1996), 77-99.

M.S. Liou, A sequel to AUSM:AUSM+, Journal of Computational Physics, 129 (1996), 364-382.

X.D. Liu, S. Osher and T. Chan, Weighted essentially non-oscillatory schemes, Journal of Computational Physics, 115 (1994), 200-212.

D.J. Mavriplis, Multigrid solution of the two dimensional Euler equations on unstructured triangular meshes, AIAA Journal, 26 (1988), 824-831.

D.J. Mavriplis and V. Venkatakrishnan, Agglomeration Multigrid for Viscous Turbulent Flows, AIAA Paper No. 94-2332, 25th AIAA Fluid Dynamics Conference, pp. 447-463, Colorado Springs, Colorado, June, 1994.

NASA - NPARC Alliance CFD Verification and Validation Web Site.

P.L. Roe, Approximatte Riemann solvers, parameter vectors, and difference schemes, Journal of Computational Physics, 43 (1981), 200-212.

C.W. Shu and S. Osher, Efficient Implementation of Essentially Non-Oscillatory Shock-Capturing Schemes, Journal of Computational Physics, 77 (1988), 439-471.

T. Sonar, On the construction of essentially non-oscillatory finite volume approximations to hyperbolic conservation laws on general triangulations: polynomial recovery, accauracy and stencil selection, Comput. Methods Appl. Mech. Engr., 140 (1997), 157-181.


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